Dynamics-based system noise adaption of an extended Kalman Filter for GNSS-only kinematic processing

An emerging application field for GNSS measurements are outdoor sports, where there is an actual need for highly accurate trajectory estimation, including velocity for training and research. In this case a Kalman filter is a useful tool to estimate the state vector using noisy observations. Typically the accuracy of the estimated quantities is described by the error covariance matrix. However, this matrix correctly represents the accuracy if all assumed models approximate the reality sufficiently well. Difficulties arise particularly when modelling the system noise, with limited knowledge about the expected dynamics. We propose a method for assessing the accuracy of the filter output without need for a ground truth. The assessment uses extensive numerical simulations based on real GNSS observations and allows analyzing the impact of model choices, noise parameters and dynamics on the accuracy of the filter output. The method is then applied to test different filter settings and chosing the most appropriate one. Since this research considers alpine skiing as a specific application, measurements from an alpine skiing training are used as basis for the investigation. We show how the above simulation method can be used to determine optimum adaptive for each epoch and how much this improves the accuracy as compared to various other strategies. Once the optimal spectral noise density is available over the whole trajectory from this analysis, we approximate it in closed form using the magnitude of the acceleration and the 3D curvature. The resulting dynamics-based system noise adaption yields virtually the same velocity accuracy as the optimum noise, and 10% to 37% better results than the other tested approaches.